Collapsing Categories is Often More Advantageous than Modeling Sparse Data: Investigations in the CFA Framework

When questionnaires include Likert scales, items endorsed by relatively few respondents may result from characteristics of examinees or the constructs under study. Researchers may collapse categories to increase cell sample size; however, effects of this practice have not been systematically investigated. A five-point ordinal scale was simulated where data included few responses in extreme categories. Different estimators were applied to sparsely distributed and collapsed category data; characteristics of sample size, number of categories, number of items including sparse data, and percentage of sparse data were manipulated. Collapsing categories were advantageous for ULSMV and WLSMV, yielding higher convergence rates, more accurate estimation of parameters and standard errors, and chi-square test rejection rates close to the nominal level. With many response categories (e.g., ≥5), treating sparse data as continuous and using MLMV may serve as an alternative, especially when a small percentage of total items contain low cell frequencies.